Low-loss dielectric resonator having a lattice structure with a resonant defect

ABSTRACT

A dielectric resonator comprising a resonant defect structure disposed in a lattice structure formed of a plurality of multi-dimensional periodically arranged dielectric elements confines electromagnetic energy within a frequency band in the photonic band gap. The frequency band of the confined electromagnetic energy is tunable. The unique structure of the dielectric resonator leads to reduced power dissipation losses when used in microwave and millimeter wave components. Accordingly, the dielectric resonator 
     BACKGROUND 
     This invention was made with government support under Contract Number N00014-86-K-0158 awarded by the Department of the Navy and Contract Number DAAL-03-86-K-0002 awarded by the Department of the Army. The government has certain rights in the invention.

BACKGROUND

This invention was made with government support under Contract NumberN00014-86-K-0158 awarded by the Department of the Navy and ContractNumber DAAL-03-86-K-0002 awarded by the Department of the Army. Thegovernment has certain rights in the invention.

Resonant cavities form an essential part of many microwave componentsincluding filters, waveguides, couplers and power combiners. A typicaldielectric resonator for a microwave integrated circuit comprises ametallic box enclosing a disk of dielectric material deposited on asubstrate with a much smaller dielectric constant. Dielectric materialsare favored for most microwave applications because the high dielectricconstants available through some materials make compact circuitcomponents possible.

These compact microwave components, however, are realized at the cost ofpower dissapation. Practical microwave integrated circuits are lossycompared to metallic resonant cavities, suffering power losses throughthe following two principle mechanisms. Since practical dielectrics arefar from lossless, power is dissipated through the induced polarizationof the dielectric material in a time-harmonic electric field. Also,practical dielectrics do not completely confine electromagneticradiation, so a conductive metallic shielding surrounds the resonator toreduce radiation losses. The shield has a non-zero resistivity whichresults in ohmic power dissipation.

SUMMARY OF THE INVENTION

It is known that a three-dimensional periodic dielectric structurehaving the proper symmetry can perfectly reflect incidentelectromagnetic radiation, incident from any orientation, within afrequency band producing a photonic band gap. Thus, electromagneticenergy at frequencies within the band gap is prohibited from propagatingthrough the structure. In accordance with the present invention, adielectric resonator comprises a resonant defect structure positioned ina lattice structure formed of a plurality of multi-dimensionalperiodically related dielectric elements which are disposed in adielectric background material. The resonant structure confineselectromagnetic energy within a frequency band in the photonic band gap.More specifically, electromagnetic energy having frequencies near theresonant frequency of the defect structure is stored within the resonantstructure. Significantly, a dielectric resonator that employs thisunique structure provides a reduced power dissipation over conventionaldevices, leading to more efficient performance.

The dielectric resonator lattice structure has a preferred diamondcrystal symmetry, although any face-centered cubic lattice arrangementmay be used. The periodically related dielectric elements may compriseoverlapping spheres of a high-dielectric material. Since the spheresoverlap, the background material may comprise air or an equivalentlow-dielectric material. Alternatively, the dielectric elements may bespherical regions of air or an equivalent low-dielectric materialpositioned in a high-dielectric background material.

In either case, the resonant defect structure is positioned in thelattice structure creating a resonant defect within the resonator. Theresonant defect structure may be comprise air or a dielectric material.Further, a coupling means may be coupled to the resonant cavity. Thecoupling means may comprise a first waveguide for couplingelectromagnetic energy to the resonant structure and a second waveguidefor coupling electromagnetic energy out of the resonant structure.

By positioning the defect structure in the dielectric resonator,electromagnetic energy in a narrow frequency band within the photon bandgap propagating through the resonator is coupled into the defectstructure. Once inside the defect structure, this energy remainstrapped. Since the resonant frequency of the defect structurecorresponds to the center frequency of the frequency band of the storedenergy, the frequency band may be tuned during construction of theresonator. Course tuning may be accomplished by choosing a diamondlattice constant which centers the photonic band gap on the desiredresonant frequency. Fine tuning may be accomplished by changing the sizeof the defect structure. Additionally, a fabricated resonator may betuned by magnetizing the dielectric background material. Morespecifically, the magnetized background material effectively shifts theentire frequency band of stored electromagnetic energy.

The present invention also comprises two methods for manufacturing adielectric resonator. One method is directed toward manufacturing aresonant structure comprised of a plurality of periodically related airspheres in a high-dielectric backing material. The other method is formanufacturing a dielectric resonator comprising overlapping periodicallyrelated high-dielectric spheres in a low dielectric environment.

Although localized electromagnetic energy in a narrow freqency band iscommon in metallic cavities, narrow frequency band electromagneticenergy stored within an entirely dielectric medium is a novelphenomenon. To that end, the present invention exploits this effect toprovide high quality resonant cavities, filters, resonant absorbers andpower generators in the microwave and millimeter wave regions.

DETAILED DESCRIPTION OF THE DRAWINGS

In the enclosed drawings like reference characters refer to the sameparts throughout the different views. The drawings are not necessarilyto scale, emphasis instead being placed upon illustrating the principlesof the present invention.

FIG. 1 is a schematic illustration of a three-dimensional diamondcrystal lattice structure.

FIGS. 2A-2C are perspective views of three-dimensional dielectricresonators in accordance with the present invention.

FIG. 3 is a graph showing the relationship between resonant frequencyand defect radius.

FIG. 4A is a graph showing the relationship between the density ofstates and frequency.

FIG. 4B is a graph showing the relationship of the bandwidth forincreasing impurity separations.

FIG. 5 is a perspective view illustrating a dielectric resonator havingcoupling means coupled to the resonant cavity.

FIG. 6A is a plan view of the periodic pattern of elements for tworepresentative sheets which are assembled to form a dielectricresonator.

FIG. 6B is a plan view of a sheet illustrating the coupling means.

FIG. 6C is a plan view illustrating the arrangement of the sheets inmanufacturing a dielectric resonator.

FIG. 7A is a cross-sectional view of an assembled dielectric resonator.

FIG. 7B is an alternative cross-sectional view of an assembleddielectric resonator.

FIG. 8 is a perspective view illustrating a three-dimensional dielectricresonant cavity constructed from a dielectric resonator.

FIG. 9 is a perspective view illustrating a three-dimensional dielectricbandpass filter.

FIG. 10A is a perspective view illustrating a dielectric absorber.

FIG. 10B shows a representative structure in which the dielectricabsorber of FIG. 10A is positioned.

FIG. 11 is a perspective view illustrating a dielectric power generator.

FIG. 12 shows the decay of the localized electromagnetic field near thedefect structure.

DETAILED DESCRIPTION OF THE INVENTION

In accordance with the present invention, a skeletal structure of athree-dimensional dielectric lattice 16 is shown in FIG. 1. A pluralityof nodes 18 represent the preferred location of the periodicallyarranged dielectric elements in the lattice. A number of lines 28 areshown to illustrate the symmetry of the lattice 16. Alternatively, thenodes 18 may be positioned at the midpoint of each line 28. Nodes 21-26signify the elements which surround a resonant defect cavity (not shown)in the preferred embodiment. As shown in FIG. 1, the nodes 18 of thelattice 16 form a crystal with diamond lattice symmetry. However, itshould be noted that any lattice with three-dimensional periodicity iswithin the scope of the present invention.

As shown in FIG. 2A, a dielectric resonator 29 has a three-dimensionaldielectric lattice structure comprised of a plurality of overlappingdielectric spheres 30 having a diamond lattice symmetry. Althoughspherical dielectric elements are used in the preferred embodiments, anyshaped element may be employed without departing from the scope of thepresent invention. A background dielectric material 37 is located in theinterstital regions around the spheres 30. In this embodiment, thespheres 30 are simply regions of air or any low-loss, low-dielectricconstant material periodically arranged in a high-dielectric backgroundmaterial 37. A resonant defect 38 surrounded by air spheres 31-36comprises an extra hole in the background material.

Alternatively, a dielectric resonator 39, shown in FIG. 2B, has athree-dimensional diamond lattice structure comprising a plurality ofoverlapping high-dielectric spheres 40 arranged to form a diamondlattice symmetry. Since the spheres 40 overlap, the interstital regions49 of the lattice 39 may comprise air. A resonant defect cavity 48 maybe formed by milling away a portion of adjacent spheres 41-46. Analternative resonant defect cavity 148 may be disposed between twospheres as shown in FIG. 2C. The cavity 148 is formed by milling awayportions of dielectric spheres 45 and 46. In any of the resonatorconfigurations of FIGS. 2A-2C, the resonant defect cavity serves toconfine electromagnetic energy within a frequency band in the photonicband gap as long as the dielectric constant of the spheres issubstantially different from the background material. Also, in any ofthe above-described configurations, the resonant defect cavity maycomprise air or any low-dielectric material or a high-dielectricmaterial.

In accordance with one feature of the present invention, for any of thedielectric resonators in FIGS. 2A-2C, the frequency band ofelectromagnetic energy within the photonic band gap stored by theresonant defect cavity may be tuned during construction of theresonator. As explained previously, the resonant frequency of the cavitycorresponds to the center frequency of the frequency band of storedelectromagnetic energy. Two parameters affect the cavity's resonantfrequency: the diamond lattice constant and the size of the defectcavity. Referring to FIG. 1, a diamond lattice constant (a) for thediamond crystal lattice 16 equals the distance between the centers oftwo elements of a crystal, corresponding to the length between elements23 and 27. The diamond lattice constant is inversely proportional to thefrequency range of the photonic band gap. In fact, the photonic band gapcenter frequency (f_(p)) may be approximately determined by thefollowing equation: ##EQU1## where ε=average dielectric constant of thelattice plus its background material and

c=speed of light.

Thus, coarse tuning of the cavity resonant frequency is accomplished bychoosing a diamond lattice constant which centers the photonic band gapon the desired resonant frequency. The actual location of the resonantfrequency of the cavity inside the photonic band gap is related to thesize of the defect. FIG. 3 shows the relationship between the radius ofthe resonant defect cavity and its resonant frequency. For a cavityresonator 29 having air spheres 30 in a high-dielectric backgroundmaterial 37 (FIG. 2A) or for a cavity resonator 39 havinghigh-dielectric spheres 40 in air (FIGS. 2B-2C), the radius of an aircavity 38 or 48 is proportional to its resonant frequency.Alternatively, for a cavity resonator having high-dielectric spheres inan air environment or air spheres in a high-dielectric environment, theradius of a high-dielectric cavity is inversely proportional to itsresonant frequency. In either case, fine tuning of the cavity resonancefrequency within the band gap is accomplished by changing the defectsize.

Another important feature of the present invention is the ability of theresonant cavity to confine electromagnetic energy in a narrow frequencyband within the photonic band gap as shown in FIG. 4A. A perfectthree-dimensional dielectric structure having diamond lattice symmetry(no resonant cavity) reflects electromagnetic energy from any incidentorientation, thereby creating a photonic band gap which is representedby dashed line in FIG. 4A. By putting a resonant defect cavity in thedielectric structure, energy within a narrow frequency band coupled intothe cavity is trapped. No matter how it propagates once inside thecavity, it is reflected back due to the periodic arrangement ofspherical elements. This feature is also shown in FIG. 4A. The densityfunction is loosely related to the resonant frequency of the cavity. Forall electromagnetic wave vector orientations for a given frequency, thedensity function averages the transmissivity of the cavity. Thus, thecavity exhibits a large transmissivity at the edge frequencies of thephotonic gap. However, inside the gap there is no transmission exceptnear the resonant frequency of the cavity (ω_(b)). The graph shows afairly broad spread about ω_(b) which is due to calculation limitations.In practice, the spread can be narrowed by increasing the number ofperiodic spherical elements surrounding the cavity.

Until now, the dielectric resonator has been described without anydiscussion as how energy is coupled into the resonant cavity. As shownin FIG. 5, a generic two-port resonator device can be constructed fromthe dielectric resonator 29 by adding a coupling means to the cavity 38.Two paths to the cavity are formed by milling through the two adjacentdielectric spheres 32 and 35. The paths are filled with ahigh-dielectric material. Thus, by making a small modification in thelattice structure, input and output paths are formed for coupling energyto the resonant cavity. Preferably, dielectric waveguides 50a and 50bare placed in the paths, each connecting to the cavity. As a result, theinput waveguide 50a provides a path for electromagnetic energy into thecavity, and the output waveguide 50b provides an path for narrowfrequency band electromagnetic energy from the cavity.

There are a number of different methods for manufacturing a dielectricresonant structure ranging from arranging spherical elements as athree-dimensional structure to drilling holes in sheets of a substrate.The following is a method for manufacturing a resonant structurecomprised of periodically related air spheres in a high-dielectricsubstrate. As shown in FIGS. 7A-7B, a representative dielectricresonator may be constructed from a plurality of stacked sheets ofsubstrate. While seven sheets are used for this embodiment, any numberof sheets can be used without departing from the scope of thisinvention.

Referring to FIG. 6A, hemispheres 58 and 60 are drilled in a squarepattern into the top and bottom of each sheet respectively. Thehemispheres 58 drilled into the top of each sheet are displaced from thehemispheres 60 drilled in the bottom of each sheet. The length ofdisplacement corresponds to the lattice constant (a) such that the finalstructure represents a three-dimensional diamond crystal lattice ofperiodic air spheres separated by a distance (a). The drilling patternfor adjacent sheets is rotated ninety degrees. Thus, every other sheethas the drilling pattern of sheet 54 while the remaining sheets have thedrilling pattern of sheet 56. As shown in FIG. 6B, a sheet 57, which isa modified version of the sheet 54, has the resonant cavity 38 and twochannels for the coupling waveguides 50a and 50b.

The sheets shown in FIG. 6C are assembled to form resonator 29 having adiamond crystal lattice structure of periodically arranged air spheres30 as shown in the sectional view in FIGS. 7A-7B. To accomplish this,first sheet 56 is positioned on first sheet 54 such that the hemispheres60 in the bottom of first sheet 56 are aligned with the hemispheres inthe top of first sheet 54. A sheet 56r, which is a sheet 56 rotatedninety degrees, is positioned on top of the first sheet 56 such that therespective hemispheres are aligned. Sheet 57 of FIG. 6B is rotatedninety degrees and stacked onto sheet 56r, and a second sheet 54 ispositioned on sheet 57. The first two steps are then repeated for theremaining sheets 56 and 56r. The resulting dielectric resonator 29 maybe mounted on a substrate or copper or it may be enclosed inside ametallic cavity.

Alternatively, a resonant structure 39 comprised of overlappingperiodically related high-dielectric spheres in an low-dielectricenvironment such as air can be assembled based on a procedure describedbelow. An assembled resonant structure 29 is shown in FIG. 5. Theassembly process for making the structure 29 includes providing aplurality of identical high-dielectric spherical elements 40 which havea sufficient diameter so as to overlap each other in the assembledstructure. Preferrably, six spheres 41-46 are modified to create aresonant cavity 48 when arranged in the final structure. Additionally,holes may be drilled through two of the six spheres (43 and 46) adjacentto the resonant cavity forming a coupling path. The spheres are thenattached together forming a three-dimensional diamond crystal latticestructure. A pair of waveguides 150a and 150b may be provided, servingas input and output ports respectively.

A significant benefit of a resonant device of this invention is itslower power consumption compared to traditional devices. Generally,increasing the number of layers decreases the power consumption of theresulting resonant device. This size-power tradeoff determines theoptimum numbers for any particular device. However, any device embodyingthe resonant structure of the present invention consumes a minimalamount of power, thereby operating at maximum efficiency.

In one embodiment of the present invention, a dielectric resonant cavity62 comprises the dielectric resonator 39 surrounded by conducting plates63. As shown in FIG. 8, the resonator 39 comprises a plurality ofhigh-dielectric spheres 40 periodically arranged in a low-dielectricenvironment such as air. Six spheres 41-46 are modified to create theresonant cavity 48 in the resonant structure 39. Additionally, channelsfilled with high-dielectric material are formed in two of the sixspheres (43 and 46) adjacent to the resonant cavity form a coupling pathto the cavity. A first dielectric waveguide 150a may be inserted intosphere 46 for coupling electromagnetic energy into the resonant cavity48. Similarly, a second dielectric waveguide 150b positioned in sphere43 provides a path for narrow band electromagnetic energy from thecavity. The dielectric structure 62 may be used in microwave componentsincluding integrated circuits.

The unique structure of the dielectric resonator 39 leads to reducedpower dissipation losses by the device 62 when used in microwave andmillimeter wave components, leading to more efficient performance. Aspreviously stated, the two power loss mechanisms in existing microwavedielectric resonators are polarization loss in the dielectric materialand ohmic loss at the conducting plates. Employing a resonator that hasseveral layers of periodically arranged dielectric spheres 40 forming athree-dimensional diamond lattice surrounding the resonant cavity 48substantially confines electromagnetic radiation. This leads to a weakerfield strength at the conducting plates, translating into reduced ohmiclosses. Also, the resonator 39 stores a substantial amount of power inthe low dielectric regions 37 (air) which have negligible loss tangents.As a result, the average loss tangent for the resonator 39 is much lessthan the loss tangent for a solid high-dielectric resonator. Thus,polarization losses will be reduced.

Another embodiment of the present invention comprises a narrow bandpassfilter 250 as shown in FIG. 9. The filter comprises a three-dimensionaldiamond lattice of high-dielectric overlapping elements including theelements 240 241-246 surrounding a resonant cavity 248. The elements 240are spherically shaped and are periodically arranged in a low-dielectricbackground environment 249 such as air. Alternatively, sphericallyshaped regions of a low-dielectric material such as air may be arrangedin a high-dielectric background material without departing from thescope of this invention. The three-dimensional diamond lattice ofelements confines electromagnetic energy within a frequency band aboutthe resonant frequency of the cavity 248. Further, the resonant cavityis surrounded by several layers of elements, making the filter veryefficient at storing electromagnetic energy in the narrow passband. Adielectric waveguide 50b is coupled into the resonant cavity via element246 and provides a output path for the narrow frequency bandelectromagnetic energy confined in the resonant cavity.

As shown in FIG. 10A, a resonant absorber 200 having a narrow passbandcomprises yet another embodiment of the present invention. The absorber200 has a three-dimensional diamond lattice structure comprised ofperiodically arranged elements 230 of dielectric material disposed in ahigh-dielectric, lossy interstital material 239. Preferably, theelements 230 are spherically shaped regions of air and the lossymaterial 239 comprises ferrite. As in the previous embodiments, aresonant cavity 238 is positioned within the lattice and stores incomingelectromagnetic energy in narrow frequency band about the cavity'sresonant frequency. Further, a waveguide 50b may be coupled through theelement 236 to the resonant cavity 238 to provide an output path for theelectromagnetic energy.

Resonant absorbers such as the absorbs of FIG. 10A are used in a varietyof applications to reduce the radar cross-section of a structure.Referring to FIG. 10B, a structure 260 has an antenna element positionedbehind a window 262 recessed in a volume 264. In accordance with thepresent invention, the resonant absorber 200 shown in FIG. 10A ispositioned in the volume to attenuate microwave radiation over a broadfrequency range incident to the antenna element while providing a narrowpassband. To that end, the resonant cavity was constructed such that itsresonant frequency corresponds to the frequency of the antenna element.Thus, a narrow frequency band of microwave radiation about the frequencyof the antenna element propagates through the absorber 200 (shown inFIG. 10A). Note that the waveguide 50b (shown in FIG. 10A) may becoupled to the antenna element to increase the amplitude of the passbandradiation. Alternatively, the same result may be achieved by positioningthe antenna element within the resonant cavity. The diamond crystallattice structure of air spheres 230 (shown in FIG. 10A) absorbsincident microwave energy over a broad frequency range within thelattice structure. Except for the narrow passband frequencies, theferrite material dissipates the microwave radiation, thereby preventingan appreciable amount of energy from backscattering off the antennaelement.

In FIG. 10B, one important feature of the resonant absorber 200 (shownin FIG. 10A) is that it may be tuned to any antenna element frequency.To that end, the structure 260 may further comprises a magnetizing meanslocated adjacent to the walls of the volume 264. Magnetizing the ferritematerial 239 (as shown in FIG. 10A) changes its dielectric constantwhich ultimately shifts the frequency response of the absorber. Morespecifically, the passband frequency range along with the resonantfrequency of the cavity 238 are shifted. Thus, the resonant frequency ofthe absorber can be tuned to correspond to any desired antenna elementfrequency.

Another embodiment of the present invention comprises a high powergenerator which provides an increased power generation capabilitycompared to traditionally devices. It is known that hollow metalliccavity resonators are used in power combining techniques, where N activedevices are inserted into the cavity to generate N times the power of asingle device. As the number of devices increases, the electric fieldinside the cavity also increases. The maximum number of devices that canbe place inside the cavity is ultimately limited by the breakdown fieldof dry air which is about 2.9 kV/mm. Thus, the power generated by asystem of N devices inside the cavity corresponds to the power stored inthe cavity when the electric field reaches the breakdown value.

Referring to FIG. 11, a high power generator comprises a hollow resonantcavity 48 surrounded by a periodic arrangement of dielectric elements 40forming a three-dimensional diamond lattice structure. An active device64, such as a field-effect transistor (FET), an IMPATT or a GUNN diode,is positioned in the resonant cavity 48. A bias circuit is attached tothe active device 64 to match the device's impedance to the impedance ofthe cavity 48. A cable 68 is linked to the bias circuit to provide powerto the active device. A waveguide 50b is provided to direct power out ofthe cavity 48. As explained previously, the periodic lattice structuresurrounding the resonant cavity is highly efficient in storingelectromagnetic energy in a narrow passband, preferrably in themicrowave and millimeter wave frequency bands. As such, the powergenerator stores more power than a metallic cavity device at the sameresonant frequency when the peak electric field is the same.

Another feature of the power generator is its high efficiency whenoperated in conjuction with a solid-state oscillator (such as a FET, anIMPATT diode or a GUNN diode) to generate microwave radiation at theresonant frequency of the cavity. Typically, hollow metallic cavityresonators are used and are often operated in a pulsed mode for radartransmission. In typical resonators, cavity losses inhibit performanceby dissipating power from the oscillator. Since the power generator 70efficiently stores power in the cavity at its resonant frequency, lesspower is dissipated.

Theoretical Basis for the Invention

In order to calculate of the electromagnetic frequency spectrum of adielectric lattice structure, the electromagnetic fields may be expandedin a plane wave basis, ##EQU2## where k is in the Brillouin zone, G issummed over the reciprocal lattice, and eλ are orthogonal to (k+G).Maxwell's equations are then expressed as a simple eigenvalue equation,##EQU3## and ε_(G) ⁻¹ _(G), is the Fourier transform of the dielectricfunction ε(r). This eigenvalue equation is solved to yield the normalmode coefficients and frequencies of the electromagnetic modes. Havingsolved for H(r), the other electromagnetic fields can be determinedsimply. This technique provides a simple and powerful method to solveproblems in electrodynamics which takes full account of the vectornature of the electromagnetic radiation. Using this technique theapproximations, the finite size of the plane-wave basis and Fouriertransform grid, are improved systematically.

Although it is desireable to examine the behavior of a single defect ina lattice of infinite size, computational simplicity leads to a testsystem employing a crystal lattice structure with a finite unit cellsize. To that end, a supercell method is employed in which one defect ispositioned in a cell of eight atoms arranged in a plane the form of adiamond structure. A number of diamond cells each having a defect arelinked to form a three-dimensional diamond crystal lattice. It should benoted that diamond lattice structure having multiple defects has beenemployed during testing for computational simplicity. However, the testresults have been corrected to correspond to a crystal lattice having asingle defect in accordance with the present invention. A diamondlattice has been used for the test calculations, although the presentinvention comprises any cell structure which forms a face-centered cubiccrystal lattice. Tests have been performed using larger supercellscontaining 16 and 32 atoms and similar results were found. Supercells oftwo, four, eight and sixteen atoms containing dense impurities in theplanes have been considered in order to determine the dependence ofbandwidth on impurity separation. Based on calculations of aone-dimensional system of periodic dielectric slabs, for which an exactsolution is available, it is expected that the frequencies providedbelow are correct to within ˜2% at this plane-wave cutoff. Althoughfully converged calculations in these one-dimensional systems agreed to0.1% it has been determined that convergence in absolute frequencies wasrelatively slow in comparison to conventional electonic structurecalculations. This is attributed to the discontinuity in the firstderivative of H(r) at the dielectric surfaces. In order to calculate thedensity of photonic states D(ω), the frequencies should be sampled at 48k-points in the irreducible Brillouin zone of the eight atom unit cell,and then coarse grained the resulting frequencies. The wave dispersionrelation was also employed. The relation is as follows: ω(k)=Vk where ωis the temporal frequency of electromagnetic energy, k is the spatialfrequency of the energy and v is the speed of light in a dielectricmedium. Although it has been explicitly verified using the wavedispersion relation that ω(k)=vk at long wavelengths and therefore D(ω)≃.sub.ω.sup. 2, this is not accurately represented in D(ω) due tocoarse sampling of the Brillouin zone.

A periodic arrangement of spheres of air in a dielectric medium has beenconsidered. A material with dielectric constant of 35 and air spheres ofradius 0.29 a, where a is the conventional lattice constant of thediamond cell has also been considered. Impurities of two types have beenconsidered: air spheres in the dielectric region which were located atthe diamond hexagonal site and air spheres place at the bond-centeredsite.

Since the applicability of a band structure breaks down when an impuritydestroys the translational symmetry of the dielectric lattice, thedensity of states of the impurity system was calculated. Calculationsshow that perfect bulk diamond crystal has a gap in its photonic bandstructure. As shown in FIG. 4A, placing an air sphere at the hexagonalsite introduces a single state in the gap, ω_(b). Since there are notravelling modes in the diamond lattice at ω_(b) this must be alocalized mode. As shown in FIG. 12, calculations have shown that thefield is localized about the defect. In fact, it has been determinedthat bound states whose frequencies are in the center of the gap havedecay lengths as small as one lattice constant. It can be expected thatthis length will diverge as the bound state frequency approaches thecontinuum of extended states.

Recall that in FIG 4A the localized modes are spread over modest rangeof frequencies. This is purely an artifact of the supercell techniqueemployed. Because the technique considers an array of defect states eachof which is localized over some finite distance, there is tunnelingbetween localized states on neighboring impurities. It is this hoppingbetween defect states that introduces a non-zero width to the impurityband. For simplicity, the maximum of the defect density of states waschosen to identify the actual position of the impurity state. Referringto FIG. 4B, a relationship of the bandwidth for increasing impurityseparations is shown. This bandwidth decreases exponentially, asexpected for exponentially bound states. In an experiment, the latticehas a finite size so that the impurity mode will have some exponentiallysmall amplitude at the walls of the lattice. This allows the localizedstate to tunnel out, and introduces a finite width to the frequencyspectrum.

Qualitatively, this result may be understood by analogy with the morefamiliar case of impurities in a crystal with a band gap in itselectronic structure. Since the wavelength of light is shorter in thedielectric, these regions are analogous to a region of deep potential inthe crystal. Inserting a dielectric impurity adds an attractivepotential. Sufficiently strong potentials can pull a state out of thephotonic conduction band into the gap, and increasing the attractivecharacter causes a decrease in the bound state frequency (see FIG. 3).Similarly, adding an air sphere to the dielectric region is analogous toadding a repulsive porential which pushes a state out of the photonicvalence band. In fact, the addition of an air sphere defect to theperfect diamond lattice decreased the number of valence states by one,and it created one state in the gap. One notable difference between airand dielectric impurities has been found. While the presence of an airsphere creates a single, well defined state in the gap, the presence ofan air sphere creates a single, well defined state in the gap (thelowest of which is doubly degenerate). This is reasonable because of thelarge number of bands above the gap.

Alternately, one can understand the localized mode as athree-dimensional Fabry-Perot interferometer. Since there are nopropagating modes in the dielectric material with frequencies in thegap, it behaves as a mirror to these frequencies. The defect then issurrounded by reflecting walls, and the localized state is analogous tothe familiar resonances of a metallic cavity. Thus, many microwave andmillimeter wave applications exist for dielectric resonators.

While this invention has been particularly shown and described withreferences to preferred embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the spirit and scope of theinvention as defined by the appended claims.

We claim:
 1. A dielectric resonator comprising:a first dielectricmaterial for receiving electromagnetic energy; a lattice structurecomprised of a plurality of shaped elements comprised of a seconddielectric material and disposed in a multi-dimensional periodicarrangement within the first dielectric material to provide a range offrequencies over a band gap in which the electromagnetic energy withinthe frequency range of the band gap is prevented from propagatingthrough the lattice structure; and a resonant defect structure disposedwithin the lattice structure for introducing a lattice imperfection inthe lattice structure, the resonant defect structure providing afrequency range within the band gap in which the electromagnetic energyhaving frequencies in the frequency range within the band gap is allowedto propagate through the lattice structure.
 2. A dielectric resonator asclaimed in claim 1 further comprising a coupler connected to theresonant defect structure, the coupler having a first waveguide forcoupling the electromagnetic energy into the defect structure and asecond waveguide for coupling the electromagnetic energy havingfrequencies in the frequency range, which is allowed to propagatethrough the lattice structure, from the resonant defect structure.
 3. Adielectric resonator as claimed in claim 1 in which the latticestructure is configured in the form of a face-centered cubic crystal. 4.A dielectric resonator as claimed in claim 1 in which the latticestructure is configured in the form of a diamond lattice crystal.
 5. Adielectric resonator as claimed in claim 1 in which the first dielectricmaterial comprises air.
 6. A dielectric resonator as claimed in claim 5in which the shaped elements are spheres, each spherical element havinga diameter such that said spherical element overlaps adjacent sphericalelements upon being disposed in said multi-dimensional periodicarrangement.
 7. A dielectric resonator as claimed in claim 1 in whichthe shaped elements are spheres.
 8. A dielectric resonator as claimed inclaim 1 in which the resonant defect structure comprises a dielectriccavity.
 9. A dielectric resonator as claimed in claim 1 in which thesecond dielectric material comprises air.
 10. A dielectric resonatorcomprising:a first dielectric material for receiving electromagneticenergy; a lattice structure comprises of a plurality of shaped elementscomprising of a second dielectric material and disposed in amulti-dimensional periodic arrangement within the first dielectricmaterial to provide a predetermined frequency band gap in which theelectromagnetic energy having frequencies within the band gap isprevented from propagating through the lattice structure; a resonantdefect structure disposed within the lattice structure for providing alattice imperfection in the lattice structure, the resonant defectstructure providing a narrow frequency range within the band gap whereinthe electromagnetic energy having frequencies within the narrowfrequency range is stored within the resonant defect structure; and anoutput coupler linked to the resonant defect structure for coupling theelectromagnetic energy having frequencies within the narrow frequencyrange and being stored in the resonant defect structure therefrom.
 11. Adielectric resonator as claimed in claim 10 in which the resonant defectstructure comprises a dielectric cavity.
 12. A dielectric resonator asclaimed in claim 10 further comprising an input coupler for coupling theelectromagnetic energy into the defect structure.
 13. A dielectricresonator as claimed in claim 10 in which the frequency band gap iswithin a frequency range of 1-3000 GHz.